{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:04.164040Z",
     "start_time": "2024-12-09T13:31:00.683569Z"
    }
   },
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import torch\n",
    "from d2l import torch as d2l\n",
    "import numpy as np"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:04.194882Z",
     "start_time": "2024-12-09T13:31:04.174935Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 生成数据集\n",
    "def synthetic_data(w, b, num_examples):\n",
    "    \"\"\"生成y=Wx+b+噪声\"\"\"\n",
    "    X = torch.normal(0, 1, (num_examples, len(w)))\n",
    "    y = torch.matmul(X, w) + b\n",
    "    y += torch.normal(0, 0.01, y.shape)\n",
    "    return X, y.reshape(-1, 1)\n",
    "\n",
    "\n",
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.5\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)\n",
    "print(\"features:\", features[0])\n",
    "print(\"labels:\", labels[0])"
   ],
   "id": "1db21832a135173b",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "features: tensor([ 0.5887, -0.3489])\n",
      "labels: tensor([6.8615])\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:04.535417Z",
     "start_time": "2024-12-09T13:31:04.383626Z"
    }
   },
   "cell_type": "code",
   "source": [
    "d2l.set_figsize()\n",
    "d2l.plt.scatter(features[:, (1)].detach().numpy(), labels.detach().numpy(), 1);"
   ],
   "id": "c35caae9bc4b7774",
   "outputs": [
    {
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    }
   ],
   "execution_count": 3
  },
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   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:04.580299Z",
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   "cell_type": "code",
   "source": [
    "# 随机小批量迭代数据\n",
    "def data_iter(features, labels, batch_size):\n",
    "    num_examples = len(features)\n",
    "    # indices = np.arange(num_examples)\n",
    "    indices = list(range(num_examples))\n",
    "    random.shuffle(indices)\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "        batch_indices = indices[i:min(i + batch_size, num_examples)]\n",
    "        # 使用yield将对应batch_indices的元素作为元组返回\n",
    "        yield features[batch_indices], labels[batch_indices]\n",
    "        \n",
    "batch_size = 10\n",
    "for X, y in data_iter(features, labels, batch_size):\n",
    "    print(X, '\\n', y)\n",
    "    break"
   ],
   "id": "9b82e9a417983b62",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.0936, -2.9981],\n",
      "        [ 0.6570, -0.1571],\n",
      "        [ 1.6339, -1.8298],\n",
      "        [-1.8779, -0.9188],\n",
      "        [ 0.3906,  0.5377],\n",
      "        [ 1.3075,  0.7894],\n",
      "        [ 1.6540, -1.0390],\n",
      "        [-0.0782,  0.0216],\n",
      "        [ 0.4286, -1.1927],\n",
      "        [-1.6953, -0.3710]]) \n",
      " tensor([[14.4987],\n",
      "        [ 6.3447],\n",
      "        [14.0077],\n",
      "        [ 3.8674],\n",
      "        [ 3.4636],\n",
      "        [ 4.4156],\n",
      "        [11.3367],\n",
      "        [ 4.2578],\n",
      "        [ 9.4150],\n",
      "        [ 2.3818]])\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:04.627259Z",
     "start_time": "2024-12-09T13:31:04.613209Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 初始化模型参数\n",
    "w = torch.normal(0, 0.01, size=(2, 1), requires_grad=True)\n",
    "b = torch.zeros(1, requires_grad=True)\n",
    "w, b"
   ],
   "id": "da94f673189470ec",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[0.0022],\n",
       "         [0.0044]], requires_grad=True),\n",
       " tensor([0.], requires_grad=True))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 5
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:04.673079Z",
     "start_time": "2024-12-09T13:31:04.660083Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 定义模型\n",
    "def linreg(X, w, b):\n",
    "    return torch.matmul(X, w) + b"
   ],
   "id": "5c0d9e0d7d93aeb1",
   "outputs": [],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:04.719666Z",
     "start_time": "2024-12-09T13:31:04.705703Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 损失函数\n",
    "def square_loss(y_hat, y):\n",
    "    # return ((y_hat - y) ** 2 / 2).sum()\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2"
   ],
   "id": "43d8805354776ba2",
   "outputs": [],
   "execution_count": 7
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:04.766678Z",
     "start_time": "2024-12-09T13:31:04.753584Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 优化算法\n",
    "# 参数集合 学习率 小批量\n",
    "def sgd(params, lr, batch_size):\n",
    "    # 检查输入参数\n",
    "    if not isinstance(params, (list, tuple)):\n",
    "        raise TypeError(\"params should be a list or tuple\")\n",
    "    if lr <= 0:\n",
    "        raise ValueError(\"lr should be positive\")\n",
    "    if batch_size <= 0:\n",
    "        raise ValueError(\"batch_size should be positive\")\n",
    "    try:\n",
    "        # 使用 torch.no_grad 上下文管理器，在更新参数时不计算梯度\n",
    "        with torch.no_grad():\n",
    "            for param in params:\n",
    "                # 根据梯度下降公式更新参数\n",
    "                param -= lr * param.grad / batch_size\n",
    "                # 将参数的梯度置零，为下一次梯度计算做准备\n",
    "                param.grad.zero_()\n",
    "    except Exception as e:\n",
    "        print(f\"Error occurred: {e}\")\n"
   ],
   "id": "28e67ea82e05d1c5",
   "outputs": [],
   "execution_count": 8
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:31:07.142602Z",
     "start_time": "2024-12-09T13:31:07.050690Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 训练\n",
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = square_loss\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    for (X, y) in data_iter(features, labels, batch_size=10):\n",
    "        l = loss(net(X, w, b), y)\n",
    "        # 因为l形状是(batch_size,1)，而不是一个标量。l中的所有元素被加到一起，并以此计算关于[w,b]的梯度，如果损失定义时就sum了，此处就不用sum\n",
    "        l.sum().backward()\n",
    "        sgd([w, b], lr, 10)\n",
    "\n",
    "    with torch.no_grad():\n",
    "        train_loss = loss(net(features, w, b), labels)\n",
    "        print(f\"epoch {epoch + 1},train loss: {train_loss.mean():.10f}\")"
   ],
   "id": "9ddf55fc978d0e3a",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1,train loss: 0.0281265993\n",
      "epoch 2,train loss: 0.0000931729\n",
      "epoch 3,train loss: 0.0000486736\n"
     ]
    }
   ],
   "execution_count": 9
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T13:58:26.967837Z",
     "start_time": "2024-12-09T13:58:26.949511Z"
    }
   },
   "cell_type": "code",
   "source": [
    "print(f'w的估计误差:{true_w - w.reshape(true_w.shape)}')\n",
    "print(f'b的估计误差:{true_b - b}')"
   ],
   "id": "b31cf601f103352b",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w的估计误差:tensor([ 0.0002, -0.0003], grad_fn=<SubBackward0>)\n",
      "b的估计误差:tensor([-5.9605e-05], grad_fn=<RsubBackward1>)\n"
     ]
    }
   ],
   "execution_count": 11
  }
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